Motorcycles generally have primary suspension systems at each end of the frame for the front and/or for the rear wheels. A seat is mounted on the frame for the rider, the seat having foam padding or small springs built into it to reduce the effect of vertical frame motion on the rider. However, otherwise the seat is fixed relative to the motorcycle frame, and there is no known secondary suspension system for the seat, which works in conjunction with the primary suspension systems. No known system exists in which the seat is supported with a degree of freedom of motion relative to the motorcycle frame, or in which the seat is kinematically linked to the rear suspension system to move relative to the frame. Linkages and components incorporated in the various embodiments of this invention of course were known, but those linkages or components were never proposed to accomplish the function realized by the invention to be disclosed.